Verify the Ampere’s law for magnetic field of a point dipole of dipole moment . Take C as the closed curve running clockwise along (i) the z-axis from z = a 0 to z = R; (ii) along the quarter circle of radius R and center at the origin, in the first quadrant of x-z plane; (iii) along the x-axis from x = R to x = a, and (iv) along the quarter circle of radius an and center at the origin in the first quadrant of x-z plane.

Question

Verify the Ampere’s law for magnetic field of a point dipole of dipole moment . Take C as the closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R; (ii) along the quarter circle of radius R and center at the origin, in the first quadrant of x-z plane; (iii) along the x-axis from x = R to x = a, and (iv) along the quarter circle of radius an and center at the origin in the first quadrant of x-z plane.

Philoid · Accepted Answer

Magnetic field induction at a point at distance r from the magnetic dipole is

i) Along z-axis from P to Q

… (1)

ii) Along the quarter circle QS of radius R is given in the figure below

… (2)

iii) Along x-axis over path ST

.... (3)

Since angle between (-M) and dl is 90 degrees.

iv) Along the quarter circle TP of radius a.

= …(4)